Bayern Munich and Borussia Dortmund remain neck and neck at the top of the German Bundesliga table after 2-1 wins over Mainz and Elversberg on Saturday.
Bayern and Dortmund, who drew 2-2 in Munich last Saturday, are locked on 21 points, with the defending champions ahead on goal difference after nine rounds.
Phillip Tietz's stoppage-time goal came too late for the hosts to try and mount a comeback as Bayern won for just the third time in their past seven Bundesliga matches at Mainz.
Goalless in three games since winning the Ballon d'Or in late October, Kane set up Joshua Kimmich's opener after 14 minutes and laid on a second-half goal for Lennart Karl.
The England captain has continued to show his prowess as a provider this season and has 10 assists to go with 10 goals in all competitions.
Kimmich told DAZN he was thrilled Kane had extended his contract at the club until 2029 on Thursday.
"He's one of the reasons why things just click in the dressing room. He's a Ballon d'Or-level player, yet he's never above doing the little things.
"He's the type of person who is always there for every single teammate. And that is truly something very, very special."
Bayern, who won 2-0 at Atletico Madrid in midweek, continue to defy a mounting absentee list.
Without coach Vincent Kompany as he returns from illness, they were also missing Jamal Musiala, Luis Diaz, Ismael Saibari and Serge Gnabry.
Kimmich returned from bereavement leave last week after the death of his father and was visibly emotional after scoring the opener.
"Naturally, the moment I scored, that was the first thing that came to mind.
"So, it was definitely more emotional than usual... Besides, I don't score that many anyway."
Manuel Neuer became the oldest player in Bayern's history when he took the pitch aged 40 years and 225 days, but was substituted before halftime with a foot injury.
NMECHA BRACE FOR DORTMUND
In Dortmund, Felix Nmecha bagged a second-half brace as the hosts beat Elversberg, but a Noel Futkeu goal with nine minutes remaining had the hosts sweating in the dying stages.
Both of Nmecha's goals came from outside the box as Dortmund overcame the absence of striker Serhou Guirassy and the early replacement of in-form forward Carney Chukwuemeka.
"It might sound boring, but we just need to go from game to game," Nmecha said of a potential title race.
"It's a very long season but we need to keep going like this."
In Saturday's late game, Stuttgart won 1-0 at home against Werder Bremen thanks to an early goal from Maximilian Mittelstaedt.
Recalled to Jurgen Klopp's Germany squad in midweek, Bundesliga top goalscorer Niclas Fuellkrug missed out on scoring for a club record eighth-straight match.
RB Leipzig conceded inside the opening minute but bounced back to beat Augsburg 5-2, continuing their excellent home form to climb to third.
Leipzig, who lost 3-2 to Manchester City at home in the Champions League on Wednesday, sit three points behind Bayern and Dortmund.
Leipzig had not conceded at home in the league this season but were behind after just 36 seconds when Anton Kade pounced on a Willi Orban error.
The hosts recovered quickly and cruised to victory, with Ezechiel Banzuzi, Christopher Nkunku, David Raum, Romulo and Christoph Baumgartner all getting on the scoresheet for Leipzig.
Uchenna Ogundu scored a late consolation for Augsburg.
Leipzig have won five from five Bundesliga games at home, scoring 23 goals and conceding just twice.
Elsewhere, Jonathan Burkardt scored twice as Eintracht Frankfurt drew 2-2 at promoted Paderborn.